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antoniya [11.8K]

3 years ago

11

What would (2,2) be as a Equation??

1 answer:

ololo11 [35]3 years ago

4 0

Y=x i hope this helps you!

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The intensity of light with wavelength λ traveling through a diffraction grating with N slits at an angle θ is given by I(θ) = N

Ymorist [56]

Answer:

0.007502795

Step-by-step explanation:

We have

N = 10,000

$\bf d=10^{-4}$

$\bf \lambda = 632.8*10^{-9}$

Replacing these values in the expression for k:

$\bf k=\frac{\pi Ndsin\theta}{\lambda}=\frac{\pi10^4*10^{-4}sin\theta}{632.8*10^{-9}}=\frac{\pi 10^9sin\theta}{632.8}$

So, the intensity is given by the function

$\bf I(\theta)=\frac{N^2sin^2(k)}{k^2}=\frac{10^8sin^2(\frac{\pi 10^9sin\theta}{632.8})}{(\frac{\pi 10^9sin\theta}{632.8})^2}$

The <em>total light intensity</em> is then

$\bf \int_{-10^{-6}}^{10^{-6}} I(\theta)d\theta=\int_{-10^{-6}}^{10{-6}}\frac{10^8sin^2(\frac{\pi 10^9sin\theta}{632.8})}{(\frac{\pi 10^9sin\theta}{632.8})^2}d\theta$

Since $\bf I(\theta)$ is an <em>even function</em>

$\bf \int_{-10^{-6}}^{10^{-6}} I(\theta)d\theta=2\int_{0}^{10^{-6}}I(\theta)d\theta$

and we only have to divide the interval $\bf [0,10^{-6}]$ in five equal sub-intervals $\bf I_1,I_2,I_3,I_4,I_5$ with midpoints $\bf m_1,m_2,m_3,m_4,m_5$

The sub-intervals and their midpoints are

$\bf I_1=[0,\frac{10^{-6}}{5}]\;,m_1=10^{-5}\\I_2=[\frac{10^{-6}}{5},2\frac{10^{-6}}{5}]\;,m_2=3*10^{-5}\\I_3=[2\frac{10^{-6}}{5},3\frac{10^{-6}}{5}]\;,m_3=5*10^{-5}\\I_4=[3\frac{10^{-6}}{5},4\frac{10^{-6}}{5}]\;,m_4=7*10^{-5}\\I_5=[4\frac{10^{-6}}{5},10^{-6}]\;,m_5=9*10^{-5}$

<em>By the midpoint rule</em>

$\bf \int_{0}^{10^{-6}}I(\theta)d\theta\approx\frac{10^{-6}}{5}[I(m_1)+I(m_2)+...+I(m_5)]$

computing the values of I:

$\bf I(m_1)=I(10^{-5})=\frac{10^8sin^2(\frac{\pi 10^9sin(10^{-5})}{632.8})}{(\frac{\pi 10^9sin(10^{-5})}{632.8})^2}=13681.31478$

$\bf I(m_2)=I(3*10^{-5})=\frac{10^8sin^2(\frac{\pi 10^9sin(3*10^{-5})}{632.8})}{(\frac{\pi 10^9sin(3*10^{-5})}{632.8})^2}=4144.509447$

Similarly with the help of a calculator or spreadsheet we find

$\bf I(m_3)=3.09562973\\I(m_4)=716.7480066\\I(m_5)=211.3187228$

and we have

$\bf \int_{0}^{10^{-6}}I(\theta)d\theta\approx\frac{10^{-6}}{5}[I(m_1)+I(m_2)+...+I(m_5)]=\frac{10^{-6}}{5}(18756.98654)=0.003751395$

Finally the the total light intensity

would be 2*0.003751395 = 0.007502795

8 0

3 years ago

If you borrow $100 for 3 years at a annual interest rate 9% how much will you pay altogether ?

katrin [286]

Answer:

$109

Step-by-step explanation:

<u>Formulas</u>

interest = (principal amount)(rate)(time)

<em>interest = (100)(0.09)(3) = $27</em>

total = principal amount + interest

<em>total = 100 + 9 = $127</em>

5 0

3 years ago

Evaluate this expression for x=-5 and y=-5

Talja [164]

Answer:

$x - 2y=5$

Step-by-step explanation:

Given

$x = -5; y=-5$

$x - 2y$ --- missing from question

Required

Evaluate

We have:

$x - 2y$

Substitute for x and y

$x - 2y=-5 - 2*-5$

$x - 2y=-5 +10$

$x - 2y=5$

3 0

3 years ago

If 2.2 pounds of a certain grain cost $1.54, how much will 5.7 pounds of the grain cost? A. $4.38

sweet-ann [11.9K]

It's D, you have to divide 1.54$ by 2.2pounds, then you will get the price for 1 pound. And then multiply the price (0,7$) by 5,7 pounds

7 0

4 years ago

Read 2 more answers

From home to school it is 24 miles. How many inches is this

Natalka [10]

Hiya! Woah this is a weird conversion but here we go... that’s like 1,520,640 inches!
Haha.
Happy to help! Bye.
~Brooke❤️

8 0

3 years ago